Answer:
Explanation:
Solution:
For a sample size of 21 and a confidence level of 95%, the degrees of freedom for the Chi-Square distribution are (n-1) = 20. We can find the critical values of Chi-Square using a Chi-Square distribution table or a calculator.
The critical values of Chi-Square are the values that leave a probability of 2.5% in each tail of the distribution. Therefore, we need to find the Chi-Square values that correspond to a cumulative probability of 0.025 and 0.975 with 20 degrees of freedom.
Using a Chi-Square distribution table or a calculator, we get:
χ2(0.025,20) = 10.851 and χ2(0.975,20) = 31.410
Therefore, the answer is (A) 10.851, 31.410.
For a 99% confidence interval for the population standard deviation, we use the formula:
(lower bound, upper bound) = (sqrt((n-1)*s^2/χ2(α/2,n-1)), sqrt((n-1)*s^2/χ2(1-α/2,n-1)))
Where n is the sample size, s is the sample standard deviation, α is the level of significance (1- confidence level), and χ2 is the Chi-Square distribution with (n-1) degrees of freedom.
Substituting the given values, we get:
(lower bound, upper bound) = (sqrt((241.6^2)/χ2(0.005,24)), sqrt((241.6^2)/χ2(0.995,24)))
Using a Chi-Square distribution table or a calculator, we get:
χ2(0.005,24) = 9.886 and χ2(0.995,24) = 45.722
Substituting these values, we get:
(lower bound, upper bound) = (1.308, 2.115)
Rounding to the same number of decimal places as the sample standard deviation, we get:
(lower bound, upper bound) = (1.3, 2.1)
Therefore, the answer is (D) (1.3, 2.1).